The Pair-Correlation Problem and the Coupled-Cluster Approach

Abstract

In the Chapters 12 and 13 we have seen how the electron correlation can be treated order by order for closed-shell and open-shell systems, respectively. It is quite obvious, however, that this approach rapidly gets very cumbersome, and —at least for open-shell systems—it is hardly feasible to go beyond the third-order energy in this way. As demonstrated in Chap. 13, higher-order terms can have quite an appreciable effect on quantities like the term splitting. Therefore, it would be highly desirable to find a more practical way of evaluating higher-order contributions. In the present chapter we shall develop such a procedure, which is based on the solution of a system of coupled differential equations of the type considered in Sect. 13.5. By considering one- and two-particle equations, it is possible to treat the dominating correlation effect, namely the pair correlation, in a complete way. This appears to be a very promising approach for an accurate treatment of the electron correlation for atomic and molecular systems.